Goal
Find a Select an equation
∆x = vot + 1/2at^2 Substitute
0.92 = 0 + 1/2a(9.5)^2 Solve
a = 0.02 rad/s^2
Goal
Find actual α Select an equation
α = a/r Substitute
α = 0.0204/0.3 Solve
α = 0.68 rad/s^2
Goal
Find percent error for experimental α Select an equation
% error = (| experimental - actual | / (experimental + actual)/2) x 100% Substitute
% error = (| 0.696 - 0.68 | / (0.696 + 0.68)/2) x 100% Solve
% error = 2.325%
The percent error shows that the experimental and actual values agree with each other reasonably.
Experiment 2 Goal
Find tension Select an equation
F = ma or T = mg Substitute
(0.23)(9.81) = T Solve
T = 2.256 N
Goal
Find experimental moment of inertia Select an equation
I = T/α Substitute
I = 0.06762/0.6962 Solve
I = 0.0971 kg*m^2
Goal
Find actual moment of inertia Select an equation
Need 3:
I = 1/3ML^2 (thin rod)
I = 1/2MR^2 (disk)
∑I = I1 + I2 + I3 Substitute
I =1/3(0.0748)(0.34)^2 (rod)
I = 1/2(0.018)(0.02125^2) (disk)
I = 5.8 x 10^-4 kg*m^2 (pulley) Solve
I = 0.0115 kg*m^2 (rod)
I = 1.6 x 10^-5 kg*m (disk)
I = 5.8 x 10^-4 kg*m^2 (pulley)
Which when substituted:
∑I = 0.0121 kg*m^2
Goal
Find percent error for experimental moment of inertia Select an equation
% error = (| experimental - actual | / (experimental + actual)/2) x 100% Substitute
% error = (| 0.0971 - 0.0121 | / (0.0971 + 0.0121)/2) x 100% Solve
% error = 155.678%
The experimental and the actual do not seem to agree at all, meaning there must have been a large error in the experiment.
Experiment 3 Goal
Find PE Select an equation
PE = mgh Substitute
PE = 0.23 x 9.8 x 0.9 Solve
PE = 2.0286 j
Goal
Find KE (translational) Select an equation
KE = 1/2mv^2 Substitute
KE = 1/2(0.23)(0.189) Solve
KE = 0.0217 j
Goal
Find KE (rotational) Select an equation
KE = 1/2Iw^2 Substitute
KE = 1/2(0.0971)(6.3)^2 Solve
KE = 1.93 j
Goal
Find KE (total) Select an equation
KE = 1/2mv^2 + 1/2Iw^2 Substitute
KE = 0.0217 + 1.93 Solve
KE = 1.9517
Goal
Find percent error for experimental energy Select an equation
% error = (| experimental - actual | / (experimental + actual)/2) x 100% Substitute
% error = (| 2.0307 - 1.9517 | / (2.0307 + 1.9517)/2) x 100% Solve
% error = 3.97%
According to the data, the energy was reasonably conserved.
Goal
Find experimental α
Select an equation
∆θ = wot + 1/2αt^2
Substitute
10π = 0 + 1/2α(9.5)^2
Solve
α = 0.696 rad/s^2
Goal
Find a
Select an equation
∆x = vot + 1/2at^2
Substitute
0.92 = 0 + 1/2a(9.5)^2
Solve
a = 0.02 rad/s^2
Goal
Find actual α
Select an equation
α = a/r
Substitute
α = 0.0204/0.3
Solve
α = 0.68 rad/s^2
Goal
Find percent error for experimental α
Select an equation
% error = (| experimental - actual | / (experimental + actual)/2) x 100%
Substitute
% error = (| 0.696 - 0.68 | / (0.696 + 0.68)/2) x 100%
Solve
% error = 2.325%
The percent error shows that the experimental and actual values agree with each other reasonably.
Experiment 2
Goal
Find tension
Select an equation
F = ma or T = mg
Substitute
(0.23)(9.81) = T
Solve
T = 2.256 N
Goal
Find experimental moment of inertia
Select an equation
I = T/α
Substitute
I = 0.06762/0.6962
Solve
I = 0.0971 kg*m^2
Goal
Find actual moment of inertia
Select an equation
Need 3:
I = 1/3ML^2 (thin rod)
I = 1/2MR^2 (disk)
∑I = I1 + I2 + I3
Substitute
I =1/3(0.0748)(0.34)^2 (rod)
I = 1/2(0.018)(0.02125^2) (disk)
I = 5.8 x 10^-4 kg*m^2 (pulley)
Solve
I = 0.0115 kg*m^2 (rod)
I = 1.6 x 10^-5 kg*m (disk)
I = 5.8 x 10^-4 kg*m^2 (pulley)
Which when substituted:
∑I = 0.0121 kg*m^2
Goal
Find percent error for experimental moment of inertia
Select an equation
% error = (| experimental - actual | / (experimental + actual)/2) x 100%
Substitute
% error = (| 0.0971 - 0.0121 | / (0.0971 + 0.0121)/2) x 100%
Solve
% error = 155.678%
The experimental and the actual do not seem to agree at all, meaning there must have been a large error in the experiment.
Experiment 3
Goal
Find PE
Select an equation
PE = mgh
Substitute
PE = 0.23 x 9.8 x 0.9
Solve
PE = 2.0286 j
Goal
Find KE (translational)
Select an equation
KE = 1/2mv^2
Substitute
KE = 1/2(0.23)(0.189)
Solve
KE = 0.0217 j
Goal
Find KE (rotational)
Select an equation
KE = 1/2Iw^2
Substitute
KE = 1/2(0.0971)(6.3)^2
Solve
KE = 1.93 j
Goal
Find KE (total)
Select an equation
KE = 1/2mv^2 + 1/2Iw^2
Substitute
KE = 0.0217 + 1.93
Solve
KE = 1.9517
Goal
Find percent error for experimental energy
Select an equation
% error = (| experimental - actual | / (experimental + actual)/2) x 100%
Substitute
% error = (| 2.0307 - 1.9517 | / (2.0307 + 1.9517)/2) x 100%
Solve
% error = 3.97%
According to the data, the energy was reasonably conserved.